Analytical Mechanics, 6 credits (TFYA40)

Main field of study

Mathematics, Applied Mathematics, Applied Physics, Physics

Course level

Second cycle

Advancement level

A1X

Course offered for

• Physics and Nanoscience, Master's Programme
• Physics and Nanotechnology
• Applied Physics and Electrical Engineering - International, M Sc in Engineering
• Applied Physics and Electrical Engineering, M Sc in Engineering
• Materials Science and Nanotechnology, Master's programme

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Modern Physics, Mechanics

Intended learning outcomes

The course represents the basic principles of classical mechanics within the framework of the variational approach. The knowledge of these principles is necessary for a deeper penetration into the structure of the classical mechanics itself, and also for a proper understanding of statistical mechanics, quantum mechanics etc. Furthermore, the methods of the analytical mechanics can serve as a set of the efficient tools for the solution of the majority of hard problems of mechanics and related topics.

To achieve this aim students should be able to

• formulate the Lagrangian function for different mechanical systems,
• solve and analyze Lagrange's equations of motion for the set of generalized coordinates,
• formulate the Hamiltonian function for different mechanical systems,
• solve Hamiltion's equations of motion for the canonical variables,
• use the generating functions to make canonical transformations.

Course content

The variational approach to mechanics, Hamilton's principle, Lagrange's equations, first integrals and conservation theorems, elimination of cyclic variables, small oscillations theory, central force problem, Hamiltonian formulation of mechanics, canonical transformations, Hamilton-Jacobi theory,Poisson bracket formulation, introduction to analytical mechanics of continuous systems.

Teaching and working methods

Lectures and seminars with the solution of problems

Examination

TEN1

Written Examination

U, 3, 4, 5

6 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Quantum Mechanics can be followed in parallel, Quantum Dynamic

Department

Institutionen för fysik, kemi och biologi

Director of Studies or equivalent

Magnus Johansson

Examiner

Iryna Yakymenko

Course website and other links

http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kk

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Course literature

Additional literature

Books

H. Goldstein, Ch. Poole, J. Safko, (2001) Classical Mechanics 3

(selected parts). Addison & Wesley

Compendiums

I.I. Yakymenko, Lecture Notes in Analytical MechanicsI.I. Yakymenko, Set of Problems in Analytical Mechanics